Can you move a single matchstick to form a valid mathematical
No sticks can be discarded, an isolated slanted stick cannot be interpreted as I (one), and a V (five) symbol must always be composed of two slanted sticks. UPDATE: The only valid symbols are Roman numerals and “+”, “-” and “=”. (Thanks Benjamin!) OK, now try this one:
If you had trouble with that last puzzle, fear not – it means your frontal lobe is probably intact! Healthy adults are frequently outperformed by patients with frontal brain damage on that test, according to a 2005 study by Reverberi et al.
The authors tested 35 patients with focal brain lesions to the lateral or medial prefrontal cortex, along with 23 age- and education-matched healthy subjects, on a series of similar “matchstick arithmetic” problems, with 3 minutes to complete each problem. Whereas only 43% of healthy subjects completed the second problem, more than 80% of the patients with lateral prefrontal damage were able to do so!
Why should this be? The authors argued that prefrontal cortex allows for “sculpting of the response space” – in other words, prefrontal cortex is used to guide and control the mental search for a solution. Normally such “cognitive guidance” is a good thing … but it can be bad for solutions which require thinking outside the box – outside the normal, real-world constraints we place on workable solutions.
So healthy adults might search for solutions that respect the rules of normal arithmetic, and assume that this constraint is implied. One might never even consider the mathematically ill-formed solution to the second problem: IV=IV=IV. On the other hand, patients with brain damage may not use these common-sense constraints, and thus be more likely to stumble upon the rather unorthodox mathematical statement which is correct in this case.
So while the frontal cortex may enable “higher” cognitive functions like planning, judgment, and goal setting, it may also constrain us. The prefrontal cortex allows us to remember our current context and our expectations of what it might entail, and project towards other contexts, both in the past and the future. Those with under-functioning frontal lobes – such as brain trauma patients, and children – may somehow live in a less-specified world, where something as simple as making coffee could be a hopelessly complex or under-determined task. Yet they may also enjoy a “cognitive drift” into mental spaces which the tight, goal-directed reins of our prefrontal cortex steer us away from.
But there’s an interesting methodological flaw in the study which allows for a less fanciful explanation (and might also explain why this paper is published in Brain instead of Nature!)
3/4 of the subjects encountered a type of matchstick problem with 10 legal moves prior to the IV=IV=IV problem – more than twice as many moves as are possible in either of the examples above. Healthy subjects might have implicitly recognized the number of potential moves, and thus avoided a time-consuming trial-and-error strategy. Lateral PFC subjects, on the other hand, might not have picked up on this rather subtle issue, and continued obliviously with a trial and error search strategy. It’s not clear to me why the authors didn’t fully balance the design to rule out such order effects (it would have been easy to do). Still, their results are interesting, regardless of why they got them.
UPDATE: See the Frontal Cortex for another example of where brain damage helps – in gambling!